Simple Epistemic Planning: Generalised Gossiping

The gossip problem, in which information (known as secrets) must be shared among a certain number of agents using the minimum number of calls, is of interest in the conception of communication networks and protocols. We extend the gossip problem to arbitrary epistemic depths. For example, we may require not only that all agents know all secrets but also that all agents know that all agents know all secrets. We give optimal protocols for various versions of the generalised gossip problem, depending on the graph of communication links, in the case of two-way communications, one-way communications and parallel communication. We also study different variants which allow us to impose negative goals such as that certain agents must not know certain secrets. We show that in the presence of negative goals testing the existence of a successful protocol is NP-complete whereas this is always polynomial-time in the case of purely positive goals.

[1]  Jelle Gerbrandy,et al.  Dynamic epistemic logic , 1998 .

[2]  Wiebe van der Hoek,et al.  A Framework for Epistemic Gossip Protocols , 2014, EUMAS.

[3]  Brenda S. Baker,et al.  Gossips and telephones , 1972, Discret. Math..

[4]  Thomas Bolander,et al.  Undecidability in Epistemic Planning , 2013, IJCAI.

[5]  Hector Geffner,et al.  Beliefs In Multiagent Planning: From One Agent to Many , 2015, ICAPS.

[6]  Yanjing Wang,et al.  A Dynamic Epistemic Framework for Conformant Planning , 2016, TARK.

[7]  Thomas Bolander,et al.  Epistemic planning for single- and multi-agent systems , 2011, J. Appl. Non Class. Logics.

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Christian J. Muise,et al.  Planning Over Multi-Agent Epistemic States: A Classical Planning Approach , 2015, AAAI.

[10]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.

[11]  Martin C. Cooper,et al.  MANAGING TEMPORAL CYCLES IN PLANNING PROBLEMS REQUIRING CONCURRENCY , 2013, Comput. Intell..

[12]  Walter Knödel,et al.  New gossips and telephones , 1975, Discret. Math..

[13]  Frank Harary,et al.  The communication problem on graphs and digraphs , 1974 .

[14]  Andreas Witzel,et al.  DEL Planning and Some Tractable Cases , 2011, LORI.

[15]  H. Landau.  The distribution of completion times for random communication in a task-oriented group , 1954 .

[16]  E. C. Milner,et al.  A Cure for the Telephone Disease , 1972, Canadian Mathematical Bulletin.

[17]  Subbarao Kambhampati,et al.  When is Temporal Planning Really Temporal? , 2007, IJCAI.

[18]  Andreas Herzig,et al.  Parameters for Epistemic Gossip Problems , 2016 .

[19]  David W. Krumme,et al.  Gossiping in Minimal Time , 1992, SIAM J. Comput..

[20]  Alex Bavelas,et al.  Communication Patterns in Task‐Oriented Groups , 1950 .

[21]  Tom Bylander,et al.  The Computational Complexity of Propositional STRIPS Planning , 1994, Artif. Intell..

[22]  Andreas Herzig,et al.  How to Share Knowledge by Gossiping , 2015, EUMAS/AT.

[23]  Emiliano Lorini,et al.  Building Epistemic Logic from Observations and Public Announcements , 2016, KR.

[24]  Richard E. Korf,et al.  Multi-Way Number Partitioning , 2009, IJCAI.